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                [HNOI2012]三角形覆盖问题                </h1>
                <p>时间限制：20s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：128MB</p>			</div>
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                                <h3>题目描述</h3><p><div style="margin: 0cm -1.1pt 0pt 36.55pt; line-height: 11.25pt; text-align: left" align="left"><span style="font-size: medium"><span style="font-family: Arial"><span style="color: black">二维平面中，给定</span><i><span style="color: black">&nbsp;&nbsp; N</span></i><span style="color: black">个等腰直角三角形（每个三角形的两条直角边分别</span></span></span></div>
<div style="margin: 0cm -1.1pt 0pt 36.55pt; line-height: 11.25pt; text-align: left" align="left"></div>
<div style="margin: 0cm -1.1pt 0pt 36.55pt; line-height: 11.25pt; text-align: left" align="left"></div>
<div style="margin: 0cm -1.1pt 0pt 36.55pt; line-height: 11.25pt; text-align: left" align="left"><span style="font-size: medium"><span style="font-family: Arial"><span style="color: black">平行于坐标轴，斜边从左上到右下）。我们用三个非负整数(<i> x</i>, <i>y</i>, <i>d</i>)来描</span></span></span></div>
<div style="margin: 0cm -1.1pt 0pt 36.55pt; line-height: 11.25pt; text-align: left" align="left"></div>
<div style="margin: 0cm -1.1pt 0pt 36.55pt; line-height: 11.25pt; text-align: left" align="left"><span style="font-size: medium"><span style="font-family: Arial"><span style="color: black">述这样一个三角形，三角形三个顶点的坐标</span></span></span></div>
<div style="margin: 0cm -1.1pt 0pt 36.55pt; line-height: 11.25pt; text-align: left" align="left"></div>
<div style="margin: 0cm -1.1pt 0pt 0cm; line-height: 1pt" align="left"><span style="font-size: medium"><span style="font-family: Arial"><span style="color: black">&nbsp;</span></span></span></div>
<div style="margin: 0cm -1.1pt 0pt 15.55pt; line-height: 11.25pt; text-align: left" align="left"><span style="font-size: medium"><span style="font-family: Arial"><span style="color: black">分别为(<i>x</i>, <i>y</i>), (<i>x</i> + <i>d</i>, <i>y</i>)</span><span style="color: black">和</span><span style="color: black">(<i>x</i>, <i>y</i> + <i>&nbsp;&nbsp;&nbsp; d</i>)</span><span style="color: black">。要求计算这</span><i><span style="color: black">&nbsp;&nbsp; N</span></i><span style="color: black">个三角形所覆盖的总面</span></span></span></div>
<div style="margin: 0cm -1.1pt 0pt 15.55pt; line-height: 11.25pt; text-align: left" align="left"></div>
<div style="margin: 0cm -1.1pt 0pt 15.55pt; line-height: 11.25pt; text-align: left" align="left"><span style="font-size: medium"><span style="font-family: Arial"><span style="color: black">积。例如，下图有</span><span style="color: black"> 3 个三角形，覆盖的总面积为 11.0。</span></span></span></div>
<div style="margin: 0cm -1.1pt 0pt 15.55pt; line-height: 11.25pt; text-align: left" align="left"><span style="font-size: medium"><span style="font-family: Arial"><span style="color: black"><img height="217" width="236" alt="" src="../file/2731_0.jpg" /></span></span></span></div></p><hr/><h3>输入格式</h3><p><p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"><span style="font-size: medium"><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">输入文件第一行为一个正整数</span><i style="mso-bidi-font-style: normal"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman">N</font></span></i><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">，表示三角形的个数。接下来</span><font face="Times New Roman"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt; mso-bidi-font-family: 宋体"><span style="mso-list: Ignore">的 </span></span><i style="mso-bidi-font-style: normal"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt">N</span></i></font></span></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"><span style="font-size: medium"><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">行每行有用空格隔开的三个非负整数，</span><font face="Times New Roman"><i style="mso-bidi-font-style: normal"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><span style="mso-tab-count: 1">&nbsp; </span>x</span></i><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt">, <i style="mso-bidi-font-style: normal">y</i><span style="mso-tab-count: 1">&nbsp;&nbsp; </span>, <i style="mso-bidi-font-style: normal">d</i></span></font><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">，描述一个三角</span></span></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"><span style="font-size: medium"><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">形的顶点坐标，分别为</span></span></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"><span style="font-size: medium"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman">(<i style="mso-bidi-font-style: normal"><span style="mso-tab-count: 1">&nbsp;&nbsp;&nbsp; </span>x</i>, <i style="mso-bidi-font-style: normal">y</i>), (<i style="mso-bidi-font-style: normal">x</i> </font></span><font face="Times New Roman"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt; mso-fareast-font-family: 'Times New Roman'"><span style="mso-list: Ignore">+ </span></span><i style="mso-bidi-font-style: normal"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt">d</span></i><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt">, <i style="mso-bidi-font-style: normal">y</i>), (<i style="mso-bidi-font-style: normal"><span style="mso-tab-count: 1">&nbsp; </span>x</i>, <i style="mso-bidi-font-style: normal">y</i>+<i style="mso-bidi-font-style: normal">d</i>)</span></font><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">，</span></span></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"><span style="font-size: medium"><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">其中</span><font face="Times New Roman"><i style="mso-bidi-font-style: normal"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><span style="mso-tab-count: 1"> </span>x</span></i><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt">, <i style="mso-bidi-font-style: normal">y</i>, <i style="mso-bidi-font-style: normal">d</i><span style="mso-tab-count: 1"> </span></span></font><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">满足</span><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman">0&le;<i style="mso-bidi-font-style: normal"><span style="mso-tab-count: 1">&nbsp;&nbsp; </span>x</i>, <i style="mso-bidi-font-style: normal">y</i>, <i style="mso-bidi-font-style: normal">d</i>&le;1000000</font></span><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">。</span></span></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"><span style="font-size: medium"><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">对于</span><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman">50%</font></span><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">的数据，</span><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman">1&le;<i style="mso-bidi-font-style: normal"><span style="mso-tab-count: 1">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>N</i>&le;500</font></span><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">；</span></span></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; mso-layout-grid-align: none"><span style="font-size: medium"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman">100%</font></span><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">的数</span><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">据，</span><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman">1&le;<i style="mso-bidi-font-style: normal">N</i>&le;10000</font></span><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">。</span><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman"> </font></span></span><span lang="EN-US" style="font-size: 10pt; color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman"><o:p></o:p></font></span></p>
<p><span style="font-size: medium">&nbsp;</span></p></p><hr/><h3>输出格式</h3><p><p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; tab-stops: 238.4pt 243.45pt; mso-layout-grid-align: none"><span style="font-size: medium"><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">仅包含一行，为一个实数</span><font face="Times New Roman"><i style="mso-bidi-font-style: normal"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><span style="mso-tab-count: 1">&nbsp;&nbsp;&nbsp; </span>S</span></i><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><span style="mso-tab-count: 1">&nbsp;&nbsp;&nbsp; </span></span></font><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">，表示所有三角形所覆盖的总面积，输出恰</span></span></p>
<p class="MsoNormal" align="left" style="margin: 0cm -1.1pt 0pt 35.95pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; tab-stops: 238.4pt 243.45pt; mso-layout-grid-align: none"></p>
<p class="MsoNormal" align="left" style="margin: 0.75pt -1.1pt 0pt 15.55pt; line-height: 11.25pt; text-align: left; mso-line-height-rule: exactly; tab-stops: 163.3pt; mso-layout-grid-align: none"><span style="font-size: medium"><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">好保留一位小数。输入数据保证</span><font face="Times New Roman"><i style="mso-bidi-font-style: normal"><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><span style="mso-tab-count: 1">&nbsp;&nbsp;&nbsp;&nbsp; </span>S</span></i><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt">&le;2^31 </span></font><span style="color: black; font-family: 宋体; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-font-kerning: 0pt">。</span><span lang="EN-US" style="color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman"> </font></span></span><span lang="EN-US" style="font-size: 10pt; color: black; mso-bidi-font-size: 12.0pt; mso-font-kerning: 0pt"><font face="Times New Roman"><o:p></o:p></font></span></p>
<p></p></p><hr/><h3>样例输入</h3><pre>3                                           .
1  1 4
2  0 2
3  2 2
</pre><hr/><h3>样例输出</h3><pre>  11.0
</pre><hr/><h3>提示</h3><p>没有写明提示</p><hr/><h3>题目来源</h3><p>day2</p>
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